^{1}, Carolyn D. Withers

^{1}, Timothy G. Wright

^{1,a)}, Kimberly I. Kaplan

^{2}, Chivone Y. N. Chapman

^{2}, Larry A. Viehland

^{2}, Edmond P. F. Lee

^{3}and W. H. Breckenridge

^{4}

### Abstract

We present high level *ab initio* potential energy curves for the complexes, where and 2; ; and , Sr, and Ra. Spectroscopic constants have been derived from these potentials and are compared with a wide range of experimental and previous theoretical data, and good agreement is generally seen. Large changes in binding energy, , and bond length, , between , , and , also found previously in the analogous complexes [M. F. McGuirk *et al.*, J. Chem. Phys.130, 194305 (2009)], are identified and the cause investigated; the results shed light on the previous results. These unusual trends are not observed for the dicationic complexes, which behave in a fashion similar to the isoelectronic alkali metal ion complexes. The potentials have also been employed to calculate transport coefficients for moving through a bath of rare gas (RG) atoms.

The work of L.A.V., K.I.K., and C.Y.N.C. was supported by the National Science Foundation under Grant No. CHE-0718024. T.G.W. is grateful for the provision of computing time under the auspices of the NSCCS. The EPSRC under Grant No. GR/S78599/02 is also thanked for funding, and A.M.G and C.D.W are grateful to the EPSRC and the University of Nottingham for the provision of studentships. We would also like to thank Professor Jack Simons for helpful discussions.

I. INTRODUCTION

II. COMPUTATIONAL DETAILS

A. Potential energy curves

B. Spectroscopic parameters

C. Ion transport coefficients

III. RESULTS

A. Spectroscopic constants

B. Trends

C. Transport coefficients

IV. DISCUSSION

V. CONCLUSIONS

### Key Topics

- Carrier mobility
- 9.0
- Electrons
- 7.0
- Ab initio calculations
- 6.0
- Barium
- 6.0
- Basis sets
- 6.0

## Figures

Variation of values for , for , Sr, Ba, and Ra, and and 2. The solid lines are for the species, and the dashed lines are for the species. Different symbols represent different metals in each case: Ca, inverted triangles; Sr, squares; Ba circles; and Ra triangles. Note the presence of a minimum in the values observed at for each of the species; but that the species do not have such a minimum. Note that has a slightly longer bond length than . See text for further discussion.

Variation of values for , for , Sr, Ba, and Ra, and and 2. The solid lines are for the species, and the dashed lines are for the species. Different symbols represent different metals in each case: Ca, inverted triangles; Sr, squares; Ba circles; and Ra triangles. Note the presence of a minimum in the values observed at for each of the species; but that the species do not have such a minimum. Note that has a slightly longer bond length than . See text for further discussion.

BS plots for and (dots) employing calculated vibrational energy levels from the potentials described in the text. The lines are obtained by employing the Morse parameters for these species from Tables I and IV, obtained from the lowest few energy levels.

BS plots for and (dots) employing calculated vibrational energy levels from the potentials described in the text. The lines are obtained by employing the Morse parameters for these species from Tables I and IV, obtained from the lowest few energy levels.

Comparison of mobility curves for (solid lines) and (dashed lines) in He at 300 K. In color, the Ca curves are in red, the Sr curves in blue, the Ba curves in green, and the Ra curves in black. If the image is in black and white, then at high the four sets of dashed lines correspond to , , , and from high to low , respectively; at low the corresponding ordering for the solid lines is , , , and

Comparison of mobility curves for (solid lines) and (dashed lines) in He at 300 K. In color, the Ca curves are in red, the Sr curves in blue, the Ba curves in green, and the Ra curves in black. If the image is in black and white, then at high the four sets of dashed lines correspond to , , , and from high to low , respectively; at low the corresponding ordering for the solid lines is , , , and

MOLDEN contour diagrams of the HOMO for each complex calculated at the RCCSD(T) values; where , Sr, Ba, and Ra. The values of the contours were selected both to show the details clearly for all complexes, and also to be as similar to each other as possible to allow comparison between the plots. The different colors indicate opposite signs of the wave function.

MOLDEN contour diagrams of the HOMO for each complex calculated at the RCCSD(T) values; where , Sr, Ba, and Ra. The values of the contours were selected both to show the details clearly for all complexes, and also to be as similar to each other as possible to allow comparison between the plots. The different colors indicate opposite signs of the wave function.

## Tables

Spectroscopic constants for calculated at the RCCSD(T) level––see text for basis sets. is the equilibrium bond length, is the depth of the potential, is the energy between the zero-point and the asymptote, is the harmonic vibrational frequency, is the anharmonicity constant, is the equilibrium rotational constant at the minimum, is the harmonic force constant, and is the spin-rotation constant. Quantities in bold are results from the present study.

Spectroscopic constants for calculated at the RCCSD(T) level––see text for basis sets. is the equilibrium bond length, is the depth of the potential, is the energy between the zero-point and the asymptote, is the harmonic vibrational frequency, is the anharmonicity constant, is the equilibrium rotational constant at the minimum, is the harmonic force constant, and is the spin-rotation constant. Quantities in bold are results from the present study.

Spectroscopic constants for calculated at the RCCSD(T) level–see text for basis sets. The symbols are defined in the header to Table I. Quantities in bold are results from the present study.

Spectroscopic constants for calculated at the RCCSD(T) level–see text for basis sets. The symbols are defined in the header to Table I. Quantities in bold are results from the present study.

Spectroscopic constants for calculated at the RCCSD(T) level–see text for basis sets. The symbols are defined in the header to Table I. All values are from the present study.

Spectroscopic constants for calculated at the RCCSD(T) level–see text for basis sets. The symbols are defined in the header to Table I. All values are from the present study.

Spectroscopic constants for calculated at the RCCSD(T) level–see text for basis sets. The symbols are defined in the header to Table I. Quantities in bold are results from the present study.

Spectroscopic constants for calculated at the RCCSD(T) level––see text for basis sets. The symbols are defined in the header to Table I. All values are from the present study.

Spectroscopic constants for calculated at the RCCSD(T) level––see text for basis sets. The symbols are defined in the header to Table I. All values are from the present study.

Spectroscopic constants for calculated at the RCCSD(T) level––see text for basis sets. The symbols are defined in the header to Table I. All values are from the present study.

Spectroscopic constants for and calculated at the RHF level, and RCCSD(T) level (in square brackets)—see text for basis sets. RCCSD(T) values are taken from Tables I and IV. All values are from the present study.

Spectroscopic constants for and calculated at the RHF level, and RCCSD(T) level (in square brackets)—see text for basis sets. RCCSD(T) values are taken from Tables I and IV. All values are from the present study.

Spectroscopic constants for and calculated at the RHF level, and RCCSD(T) level (in square brackets)—see text for basis sets. RCCSD(T) values are taken from Tables II and V. All values are from the present study.

Spectroscopic constants for and calculated at the RHF level, and RCCSD(T) level (in square brackets)—see text for basis sets. RCCSD(T) values are taken from Tables II and V. All values are from the present study.

Spectroscopic constants for and calculated at the RHF level, and RCCSD(T) level (in square brackets)—see text for basis sets. RCCSD(T) values are taken from Tables III and VI. All values are from the present study.

Spectroscopic constants for and calculated at the RHF level, and RCCSD(T) level (in square brackets)—see text for basis sets. RCCSD(T) values are taken from Tables III and VI. All values are from the present study.

Comparison of values (angstrom) for (Refs. 21–24) and .

Comparison of values (angstrom) for (Refs. 21–24) and .

Energies of the lowest states of the , , , and ions (Ref. 34). These states are formed from an excitation of the outermost electron into the orbital in each case.

Energies of the lowest states of the , , , and ions (Ref. 34). These states are formed from an excitation of the outermost electron into the orbital in each case.

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